Clean the chicken in cold water then pat dry (see notes).
Transfer the flour to a plate, add ½ teaspoon salt then mix to combine.
Coat the chicken pieces on both sides with the flour mixture, shaking off any excess flour.
Using a pan, or the pot of your Ninja Foodi set to the sauté function, heat the oil until it is hot.
Brown the chicken, skin-side down. Flip, then brown on the other side. Transfer to a plate and set this aside.
Saute onion and garlic until translucent then add the carrot, bell pepper, and celery stick. Stir to combine.
Next, add the white wine and scrape the bottom of the pan or pot to loosen any browned bits (deglaze it).
Add the tomatoes, mix, then add the chicken, capers, and chicken stock. Season with salt and pepper, then spoon some of the sauce on top.
Cover the slow cooker. Make sure the lid is set to seal, if using the Ninja Foodi Multi-cooker. Slow cook on low for 6 hours or on high for 3-4 hours.
Once the time is up, check and adjust the seasoning as necessary, then garnish with chopped parsley (optional). Serve chicken cacciatora with crusty bread, pasta dishes, rice, or as preferred.